You can't claim you've forgiven, if you haven't forgotten. Agree?
You cannot claim you've forgiven someone if you haven't forgotten. Choosing not to forget means that you still remember the bad that they've done, therefore you haven't forgiven. Choosing not to forget means that there's still some residual resentment left, and forgiveness by definition is to let go of ALL resentment. You're still remembering for a reason, otherwise you'd forget.
Forgiveness is actually very freeing. To forgive is to release your heart of poisons that only affect you. The person who you claim to have forgiven most likely doesn't know you haven't forgotten, so they're good, but when you hold onto a grudge it only makes you feel miserable. If Nelson Mandela could forgive people who robbed him of 27 years of his life, who am I not to forgive?